Supermarket Checkout Challenge
January 4th, 2008
We’ve all been there. You’re in your local supermarket, there’s a choice of queues to join at the cashiers - which do you go for? Does it always seem like the other queue is going faster? Too bad, I’m not dealing with that today.
Given the amount of time the average British person spends in queues, I had plenty of time to come up with the best strategy when it comes to getting out of the supermarket as quickly as possible. It all came about because of those “express” checkouts. I wondered: are they really faster?
Consider the fact that there are two parts that make up the total time required to pass through a checkout - scanning the items, and paying for them. The more items you have, the longer the first part will take. However, paying for 100 items takes no longer than paying for 10. So we might describe a formula for queue time like this:
Queueing time = (number of items * X) + Y
Where X is the amount of time it takes to scan one item (let’s say, 2 seconds), and Y is the amount of time it takes to pay (say, 30 seconds).
Y is always the same (more or less - I’m choosing to ignore those prats that still insist on paying by cheque) but the other half of the equation is variable. So whether there’s one person with 100 items, or 10 people with 10 items each, it will take the bored-looking cashier the same amount of time to scan all the items. However, the “express” queue will take a lot longer! See for yourself:
( 100 items * 2s ) + ( 1 paying customer * 30s ) = 230 seconds
( 100 items * 2s ) + ( 10 paying customers * 30s ) = 500 seconds
Now, I know I’ve confused you a little. One trolley load is quicker than 10 baskets? You bet your sweet ass it is. This poses another question - why call them express queues? Look at it from the supermarkets point of view - how many customers can each cashier clear in an hour? Given there’s 3,600 seconds in an hour:
customers per hour = 3,600 ÷ time for each customer
regular checkout: 3,600 ÷ 230 = 15.7
express checkout: 3,600 ÷ 500 = 7.2
Initially it looks like the express lane is slower but remember that 500 seconds is the time take for 10 customers, so this till churns through 72 customers an hour, compared to a paltry 15.7 per hour for the regular checkout. Whoa - I thought we’d already decided that express queues were slower - what’s going on? What we have here is a difference in perspective. While the supermarket is concerned with how many customers per hour it can process, you are only concerned with how long it takes you to get through the queue. So remember kids, look at the number of items in the queue, not the number of people. That’s the key to sailing through the checkouts.
* if this post gets enough praise, I might take the time to draw some little diagrams. Which will make it accessible to those plebs at Digg. In the meantime, feel free to critique my maths.
Entry Filed under: General
|
|
|
|
13 Comments Add your own
1. Silent1 | January 5th, 2008 at 4:32 am
Frank be careful, it’s a slippery slope from faux formula to paid for cack formulas, much lambasted by yourself.
2. hairnet | January 5th, 2008 at 10:57 am
I think Y should how some variance, ie +/- 20s, that would make it muh more applicable to the individual where average times are less important.
3. Frank the SciencePunk | January 5th, 2008 at 12:01 pm
@ Silent1: Yes, I will have to be careful! Although this is more a thought experiment than a real posit.
@ hairnet: don’t tempt me, or I’ll whip up some badass spreadsheets and macro functions exploring this idea. :)
4. BobP | January 5th, 2008 at 4:04 pm
Are you able to extend this theorem to tell me which lane to choose on the M4 on Monday morning in orer to minimise my journey time?
5. Joe D | January 5th, 2008 at 6:15 pm
BobP: somebody has done something about busy motorways — they applied game theory to changing lanes in heavy traffic — though I’ve forgotten the conclusions, and I don’t remember whether it was something serious or a silly thought experiment.
6. Hayden S | January 6th, 2008 at 7:17 pm
Definitely need some sweet diagrams for this.
7. Ian | January 7th, 2008 at 12:11 pm
“So remember kids, look at the number of items in the queue, not the number of people”
Didn’t you say the key factor was the number of customers? I.e. with both queues having 100 items, the express is slower as it has more people.
Anyway, you need to factor in those stupid cashiers who start blasting down the next persons items before you’ve finished packing. Didn’t anyone told them they’re paid per hour, not per customer? My answer is to defer payment until I’m packed and ready to go. Usually by this time the over-eager next customer is blocking the chip/pin machine. I hate it.
8. Frank the SciencePunk | January 7th, 2008 at 12:18 pm
@ Ian: Actually, I was thinking about that on the bus today, that something wasn’t sitting right with this article. Well done for spotting it.
And yes, Hayden is right.. sweet diagrams are needed…
9. manigen | January 8th, 2008 at 1:17 pm
One of the sweet, sweet diagrams should show the trade off between different lengths of queue. After all, what do I do if there are two trolleys on one till and fifteen baskets at the express checkout? We need your help Frank!
10. badchemist | January 9th, 2008 at 8:49 pm
Although I agree with this Frank you need to factor in the occasions when someone in front of you manages to choose the only item in the shop without a barcode/price and then insists on waiting for the assistant to go and find out even though it’s an item that really could wait until another day.
Sorry, just got back from T***o and have supermarket queue rage.
11. nick J | January 30th, 2008 at 9:01 am
There are also the nice people who at my local supermarket decide that the ability to count is a convenience not a bit of logical knowledge retained from childhood. So they hit up the express with their cart full of crap loading the half a meter of counter space up every moment the cashier pulls something across the scanner.
Self checkouts are the way of the future!
12. Frank the SciencePunk | January 30th, 2008 at 10:31 am
Whoa, self-checkouts are a whole new variable. I’d say they must be the slowest, simply because every single person has to learn how to use one as the go. They’re only “fast” in the sense that barely anyone wants to use them, so there’s no queue.
Incidentally, I refuse to use self-checkouts on the basis that I’ve already paid to have someone check my goods; and unless the supermarket it going start paying me a wage for working in their store, I’ll be damned if I’m going to start scanning items.
13. Ian | January 30th, 2008 at 11:12 am
Good man, I’m exactly the same. They’ll have us packing the shelves soon too. It’s funny how people enjoy doing simple tasks. You know like when you give an octopus a jar to open? People love queueing for the self-service even when the standard ‘express’ tills are empty!
Leave a Comment
Some HTML allowed:
<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>
Trackback this post | Subscribe to the comments via RSS Feed